# Year 8 mathematics · your ten-day work page

The examples are invented. You can show each step on paper, with labelled tiles, by typing, speaking/AAC, a tactile line or a reader who gives you the exact prompt. Choose one A/B/C route from [daily choices](DAILY-CHOICES.md). Explain **why** a move keeps two expressions equivalent or an equation balanced. A substitution checks a proposed value. Record the given domain before interpreting a model. Drawing neatness and speed are not the mathematics.

## Week 3

### Day 11 · Every term in the bracket

Three identical packs contain `x+4` cards each. Expand `3(x+4)` by showing all groups, then substitute `x=2` in both forms. For your chosen practice route, expand and check at a value. **Exit:** fix `2(z+6)=2z+6` and show what happens at `z=1`.

### Day 12 · Terms keep their signs

Simplify `4x+7+2x−3` by grouping like terms. Check at `x=2` in both original and short forms. Choose a route and show your regrouping. **Exit:** evaluate `2n+5+3n−1` at `n=2` in two ways.

### Day 13 · Reverse distribution

Use six equal groups to explain `6x+12` as a product with brackets. Expand your product to check. Choose a route. **Exit:** fill the blank in `3t+15=3(t+__)`, then test `t=1`.

### Day 14 · From total to input

A fictional kit uses `C=8+5n`, where `n` is a non-negative whole number of refills. Rearrange to make `n` the subject. Find `n` when `C=33` and verify by substituting in the original. Ask whether every possible `C` is a whole-refill total. Choose a route. **Exit:** explain `C=8` in this model.

### Day 15 · New expression transfer

Your teacher will release a **new-case check** after a short rehearsal. Save your first response. The check asks for your transformation steps, a verification and a careful interpretation. After that, use the Day15 routes for practice with **different numbers**. **Exit:** write one step you will inspect before trusting two forms as equivalent.

## Week 4

### Day 16 · Balance and substitute

Solve `3x+7=25` by doing the same operation to both sides. Check your value. Try `2y+5=12`; a fraction/decimal may be the exact answer when no whole-count rule is given. Choose a route. **Exit:** solve and check `4z−3=9`.

### Day 17 · Two relations meet

Fictional plan A uses `6+4n` tokens; plan B uses `18+2n` for `n` whole batches. Find where totals match and verify in both formulas. Plot or describe A and B using `(0,total)` and the meeting point. Choose a route. **Exit:** which is lower at seven batches and by how much? Name the unit.

### Day 18 · Values below a cap

A fictional poster desk uses `9+5n` points for `n` whole posters, with at most 34 points. Write and solve an inequality. Mark its boundary on a [number-line/graph board](print/line-and-boundary.pdf) or state the allowed integers in words. Test the boundary and one value beyond it. Choose a route. **Exit:** at your boundary, what changes if “at most” becomes “less than”?

### Day 19 · Dividing by a negative

A fictional tray has `15−3t` counters after `t` turns, where `t` is a whole number from 0 through 5. Solve “more than 3 counters remain”. Verify one accepted turn and the first excluded turn. Choose a route. **Exit:** solve `8−2u≥0` and say what domain you are using.

### Day 20 · New equation and inequality transfer

Your teacher will release a **new check** after a short rehearsal with other values. Show equations, inverse steps, boundary checks and what the model can/cannot say. A blank board, text or tactile route is available. Your first response is the formative evidence; Day20 routes come afterward. **Exit:** say one substitution you would make before using a model total.

Optional [extras/home work](DAILY-EXTRAS.md) never requires a printer or device. Do not use actual family costs or another student's data. The [full text/tactile descriptions](print/TEXT-ALTERNATIVES.md) contain every print label. Original SubjectNest learner page © NeuroForgeIO Pty Ltd 2026, [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/).